rotation_180_control
plain-language theorem explainer
The 180-degree rotation control requires that the chi-squared for a galaxy's reversed radial profile exceeds the ILG median of 2.75 from Paper II. Researchers auditing the zero-parameter SPARC falsification test cite it to confirm that profile reversal inflates the fit statistic above the baseline. The definition reduces to a direct comparison against the fixed threshold supplied by paper2_median_chi2.
Claim. Let χ²_rot be the chi-squared per degree of freedom on the 180-degree reversed radial profile. The control holds if and only if χ²_rot > 2.75.
background
The SPARC falsifier module encodes a protocol that tests the ILG rotation-curve model with every parameter locked to powers of φ. Constants are fixed at α_t ≈ 0.191, C_lag ≈ 0.090, and Υ_star = φ. Predicted curves are generated for the full SPARC sample, χ²/dof is evaluated per galaxy, and the median is compared to a threshold; the module documentation states that a value above 3.0 refutes the RS prediction.
proof idea
One-line definition that applies the strict inequality paper2_median_chi2 < chi2_rot, where paper2_median_chi2 is the constant 2.75 reported for the ILG model on the SPARC Q=1 subset.
why it matters
The definition supplies one conjunct inside all_controls_inflated, which requires every negative control (permutation, rotation, and gas-stars swap) to inflate χ² above the ILG baseline. It closes one branch of the falsification protocol in the module documentation and connects to the Recognition Science chain through the φ-locked parameters (T5 J-uniqueness and T6 phi fixed point).
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